Not Conway's 99-Graph Problem
Sa'ar Zehavi, Ivo Fagundes David de Olivera
TL;DR
This paper presents an alternative interpretation of Conway's 99-graph problem, which remains unsolved, and provides a complete solution to this reinterpretation, offering new insights into the problem.
Contribution
The paper introduces a novel reinterpretation of Conway's 99-graph problem and solves this version entirely, advancing understanding of the original problem.
Findings
Complete solution to the alternative interpretation
New insights into the structure of the 99-graph problem
Clarification of Conway's original problem context
Abstract
Conway's 99-graph problem is the second problem amongst the five 1000$ 2017 open problems set. Four out of the five remain unsolved to this day, including the 99-graph problem. In this paper we quote Conway's definition of the problem and give an alternative interpretation of it, which we humorously name "not Conway's 99-graph problem". We solve the alternative interpretation completely.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · graph theory and CDMA systems